Problem: Given $ m \angle LOM = 8x + 50$, and $ m \angle MON = 9x + 28$, find $m\angle LOM$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {8x + 50} + {9x + 28} = {180}$ Combine like terms: $ 17x + 78 = 180$ Subtract $78$ from both sides: $ 17x = 102$ Divide both sides by $17$ to find $x$ $ x = 6$ Substitute $6$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 8({6}) + 50$ Simplify: $ {m\angle LOM = 48 + 50}$ So ${m\angle LOM = 98}$.